Most of us on this site probably have at least ten years of experience, or more, in anime fandom. So my question is: If you could give a newcomer to anime advice. What would it be?

My advice would be to pace yourself. Start out watching shows in a genre that you like then branch out into others. Just because a new season of anime is airing doesn't mean that you have to watch every single show. Doing something you want to do is enjoyable. Doing something that you feel you need to do can make it seem more like a chore. Which I believe can lead to burnout.

If I think of other things I'll post them here...here's my first thought on the question at hand:

If the newcomer is someone who has a show or movie they've seen recently as a starting point then thinking up of something related to what they saw would be my next step. But, if the person has never knowingly watched any anime in the past then the story is different. In that case my choice for the "gateway drug" (so to speak) would be a Studio Ghibli movie which I think might catch the person's fancy. The perennial favourites over here seem to be "Laputa, Castle in the Sky", "My Neighbour Totoro", and "Kiki's Delivery Service". Those would be my first choices. Second choices would be "Spirited Away", "Nausicaa of the Valley of the Wind", and "Porco Rosso" from the films directed by Miyazaki Hayao and "Only Yesterday" and "Kaguya Hime no Monogatari" from the films directed by Takahata Isao.

"Boredom is not an appropriate response to exploding cars." - Hugh Laurie

That's a pretty good question. What I would do is start off on a popular anime, one with an established fanbase, like Dragon Ball Z or Naruto. You really can't go wrong with any Shonen Jump anime, in my opinion. Then maybe I would work my way down to some lesser known anime after a while, but that's just me.

^ This. I think it's best to start off with shows/books that are available where you live. For me personally, it helped that all the resources I needed were pretty much right in front of me and there were plenty of other people who liked the same things. Usually anime/manga that are popular in America end up being nostalgic "classics" like Dragon Ball, Sailor Moon, Naruto, Fullmetal Alchemist, Attack on Titan, anything by CLAMP, etc.

Also it doesn't hurt to watch every Miyazaki movie! (Kind of fits in with the above reasons.)

But yeah... I didn't realize how important the whole "taking it slowly" thing really is, because I eventually got to the point where I was managing 8+ of the current season shows every few months. It's really not the best way to go about enjoying anime, because you really get burned out, and honestly it made me start to hate a lot of shows because they repeat the same formulas.

Now I'm a lot happier finding one or two shows that I know I'll love. So much more enjoyable.